Question

What factors must you consider to determine the sign of \(\Delta S\) for the reaction \(2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)\) if it occurs at constant temperature?

Short answer

The sign of \(\Delta S\) for the reaction is positive, considering the increase in the number of gas moles from two to three at constant temperature.

Step-by-step solution

Identify the change in the number of gas moles

First, count the number of moles of gas before and after the reaction. For the reactant, there are two moles of N2O(g), and for the products, there are two moles of N2(g) and one mole of O2(g), totaling three moles.

Analyze the entropy change due to the change in moles of gas

Entropy usually increases when the number of gas molecules increases during a chemical reaction at constant temperature and pressure. In this case, the reaction results in an increase from two to three moles of gas.

Determine the sign of \(\Delta S\)

Since the reaction increases the number of gas moles from two to three, this implies an increase in the disorder of the system. Therefore, the sign of the change in entropy, \(\Delta S\), will be positive.

Key concepts

Change in Number of Gas Moles

Understanding the role of gas moles in entropy change during a chemical reaction is crucial for predicting the outcome of the process. Entropy, denoted by the symbol 'S', is a measure of the disorder or randomness within a system, and a chemical reaction that increases the number of gas moles generally leads to higher entropy. This is because gas particles are more spread out and have more ways to arrange themselves in space compared to liquids or solids.

For instance, in the reaction provided, we begin with two moles of N₂O and end up with a total of three moles of gases—two moles of N₂ and one mole of O₂. This change is significant as going from fewer to more moles of gases implies that there are more particles moving freely after the reaction, contributing to an increase in randomness, or entropy, of the system.

It's also important to note that while this concept generally holds true, the specific conditions under which the reaction takes place, such as temperature and pressures, can also affect the entropy of a system. However, at constant conditions, the increase in the number of gas moles is a strong indicator that the entropy has increased.

Entropy and Reaction Direction

The direction in which a reaction proceeds can often be influenced by changes in entropy. In chemical thermodynamics, entropy is not only a measure of disorder but also an indicator of the feasibility of a reaction proceeding spontaneously under given conditions. At constant temperature and pressure, if a reaction leads to an increase in entropy, it is more likely to proceed in the forward direction.

In our example reaction, the forward reaction increases the number of gas moles, which is generally associated with an increase in entropy; this implies that the reaction is thermodynamically favorable in the forward direction, at least from the entropy standpoint. It's essential to remember that entropy is just one part of the equation. The overall spontaneity of a reaction is determined by the Gibbs free energy change, which takes into account both entropy and enthalpy changes.

The relationship between entropy and reaction direction is a central concept in understanding why certain reactions occur under specific conditions while others do not. By examining the entropy change, we gain insight into the 'disorderly' tendencies of the reacting particles and how they may favor one direction over another.

Predicting Sign of Delta S

Predicting the sign of the change in entropy, denoted as \(\Delta S\), is vital for assessing the spontaneity and direction of a chemical reaction. A positive \(\Delta S\) indicates an increase in disorder and randomness, whereas a negative \(\Delta S\) signifies a decrease. The change in entropy can be influenced by several factors including the change in the number of moles of gases, phase changes, temperature, and mixing.

In chemical reactions involving gases, as observed in the provided exercise, an increase in the number of gas moles usually results in a positive \(\Delta S\), suggesting that the system has become less ordered. This is because gas particles have more freedom to move and occupy a larger volume when there are more moles present. In the given reaction, we move from two moles of N₂O to a total of three moles as N₂ and O₂, signifying a positive \(\Delta S\).

When using this knowledge to predict the sign of \(\Delta S\), it's also important to bear in mind that exceptional situations can occur. For example, significant energy changes during a reaction or the involvement of complex molecules can subtly influence the outcome. Thus, while the rule of thumb regarding gas moles is a great starting point, additional factors may also need to be considered for a full thermodynamic analysis.